Parallel lines have the same slope
The equation of the line is: [tex]y = -2x+8[/tex]
The equation is given as:
[tex]y = -2x + 5[/tex]
The slope intercept form of an equation is:
[tex]y = mx + b[/tex]
Where:
[tex]m \to slope[/tex]
By comparison,
[tex]m = -2[/tex]
The line is said to be parallel to [tex]y = -2x + 5[/tex].
This means that the line has a slope of [tex]m = -2[/tex]
The equation of the line is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
Where:
[tex](x_1,y_1) = (4,0)[/tex]
So, we have:
[tex]y = m(x - x_1) + y_1[/tex]
Substitute values for m, x1 and y1
[tex]y = -2(x - 4) + 0[/tex]
[tex]y = -2(x - 4)[/tex]
Open brackets
[tex]y = -2x+8[/tex]
Hence, the equation of the line is: [tex]y = -2x+8[/tex]
See attachment for the graphs of [tex]y = -2x+8[/tex] and [tex]y = -2x + 5[/tex]
Read more about equations of parallel lines at:
https://brainly.com/question/402319
